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Algebra II : Simplifying Exponents

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Example Questions

Example Question #281 : Simplifying Exponents

Simplify: $[(9^{4})^{20}]^2$

Possible Answers:

$9^{82}$

$9^{26}$

$9^{80}$

$9^{160}$

$9^{48}$

Correct answer:

$9^{160}$

Explanation:

Evaluate by using the product rule of exponents. Solve the parentheses first.

$(9^{4})^{20} = 9^{4\cdot 20} =9^{80}$

Solve the bracket.

$[(9^{4})^{20}]^2=[9^{80}]^2 = 9^{80\cdot 2} =9^{160}$

The answer is: $9^{160}$

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Example Question #95 : Distributing Exponents (Power Rule)

Simplify:

$\frac{(x^2y^3)^9}{xy^7}$

Possible Answers:

$x^{17}y^{20}$

$\frac{x^9}{y^{36}}$

$x^{10}y^5$

$x^{11}y^{27}$

Correct answer:

$x^{17}y^{20}$

Explanation:

Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

Start by simplifying the numerator:

$(x^2y^3)^9=x^{18}y^{27}$

Now, place this on top of the denominator and simplify. Recall that when you divide exponents that have the same base, you will subtract the exponent in the denominator from the exponent in the numerator.

$\frac{x^{18}y^{27}}{xy^7}=x^{17}y^{20}$

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Example Question #282 : Simplifying Exponents

Simplify: $2(2^{20})^5$

Possible Answers:

$4^{51}$

$2^{101}$

$2^{100}$

$4^{100}$

$4^{101}$

Correct answer:

$2^{101}$

Explanation:

We can solve the exponent in the parentheses first.

Use the power rule to simplify the term.

$(2^{20})^5 = (2^{20\cdot 5}) = 2^{100}$

The expression becomes:

$2(2^{20})^5 = 2(2^{100}) = 2^1 \cdot 2^{100}$

Since the bases of the powers are the same, we can add the exponents.

The answer is: $2^{101}$

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Example Question #283 : Simplifying Exponents

Simplify the exponents: 5^4(25^2)^3

Possible Answers:

$5^{48}$

$5^{14}$

5^9

$5^{40}$

$5^{16}$

Correct answer:

$5^{16}$

Explanation:

Simplify the powers in parentheses first. According to the product rule, their powers can be multiplied.

(25^2)^3 = 25^6

The expression becomes:

5^4(25^2)^3=5^4(25^6)

Convert the number 25 to base five.

$5^4(5^{2(6)}) = 5^4(5^{12})$

Since the bases are similar, the property of exponents allow us to add the exponents.

The answer is: $5^{16}$

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Example Question #281 : Simplifying Exponents

Simplify: $(3^{600})^3$

Possible Answers:

$3^{603}$

$27^{603}$

$27^{1800}$

$3^{1800}$

$9^{1800}$

Correct answer:

$3^{1800}$

Explanation:

The exponents are separated by a parentheses.

According to the distributive property of exponents, we can simply multiply the two exponents.

$3^{600\times 3} = 3^{1800}$

Do not cube the three!

The answer is: $3^{1800}$

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Example Question #285 : Simplifying Exponents

Simplify: $6(36^{10})^3$

Possible Answers:

$6^{25}$

$6^{61}$

$36^{42}$

$36^{15}$

$6^{24}$

Correct answer:

$6^{61}$

Explanation:

To simplify this expression, convert the value of 36 to base six.

$6(36^{10})^3 = 6(6^{2(10)})^3 = 6(6^{20})^3$

Evaluate the product of exponents.

$6(6^{60})$

This is similar to: $6^1 \cdot 6^{60}$

When common bases of a certain powers are multiplied, the exponents can be added.

The answer is: $6^{61}$

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Example Question #286 : Simplifying Exponents

Solve: $2(2^{19})^4$

Possible Answers:

$2^{77}$

$32^{23}$

$4^{77}$

$4^{23}$

$2^{24}$

Correct answer:

$2^{77}$

Explanation:

Evaluate the expression by using the product rule of exponents.

$2(2^{19})^4 =2(2^{19\times 4})= 2(2^{76})$

Rewrite the expression using 2=2^1 .

$2(2^{76}) = 2^1 \cdot 2^{76}$

When powers of a same base are multiplied together, we can add the exponents.

The answer is: $2^{77}$

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Example Question #282 : Simplifying Exponents

Evaluate: -(-3^2)^3

Possible Answers:

243

729

Correct answer:

729

Explanation:

To solve this expression, we can use the power property of exponents to simplify the powers.

$-(-3^2)^3=-(-3^2)(-3^2)(-3^2) = -(-3^{2(3)})= -(-3^6)$

Use order of operations to solve the inner term. Since negative three in not in a quantity itself, only the number three is raised to the power of six.

-(-3^6) = -(-729)= 729

The answer is: 729

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Example Question #287 : Simplifying Exponents

Simplify: $[4(2^{30})^5]^3$

Possible Answers:

$4^{900}$

$2^{456}$

$4^{105}$

$8^{450}$

$64^{35}$

Correct answer:

$2^{456}$

Explanation:

Evaluate the inner parentheses first. We can use the product rule of exponents to simplify this term.

$(2^{30})^5 = 2^{30\times 5} = 2^{150}$

Replace the term in the bracket.

$[4(2^{30})^5]^3= [4(2^{150})]^3$

Convert the base of the value of 4 to base two.

4=2^2

$[4(2^{150})]^3 = [2^2(2^{150})]^3 = [2^2\cdot2^{150}]^3$

The inner bracket shares common bases of a power that are multiplied. The rule of exponents allow us to add the terms.

$[2^2\cdot2^{150}]^3 = [2^{2+150}]^3 = [2^{152}]^3$

Use the product rule to simplify this term.

$[2^{152}]^3= 2^{152\times 3}$

The answer is: $2^{456}$

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Example Question #288 : Simplifying Exponents

Solve: $8(2^{30})^3(4^{10})^3$

Possible Answers:

$4^{153}$

$2^{153}$

$8^{153}$

$2^{26}$

$4^{150}$

Correct answer:

$2^{153}$

Explanation:

In order to determine the value of this expression, change all the bases to base two.

$8(2^{30})^3(4^{10})^3=(2^3)(2^{30})^3(2^{2(10)})^3 =(2^3)(2^{30})^3(2^{20})^3$

Simplify the exponents separated by the inside and outside of the ending parentheses by multiplying the terms.

$(2^3)(2^{30})^3(2^{20})^3 = (2^3)\cdot (2^{30\times 3})\cdot (2^{20\times 3})$

Multiply the exponents.

$(2^3)\cdot (2^{30\times 3})\cdot (2^{20\times 3})= (2^3)\cdot (2^{90})\cdot (2^{60})$

Now that we are multiplying the similar bases with exponents, the exponents can be added.

$(2^3)\cdot (2^{90})\cdot (2^{60})=2^{3+90+60} = 2^{153}$

The answer is: $2^{153}$

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Algebra II : Simplifying Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #281 : Simplifying Exponents

Example Question #95 : Distributing Exponents (Power Rule)

Example Question #282 : Simplifying Exponents

Example Question #283 : Simplifying Exponents

Example Question #281 : Simplifying Exponents

Example Question #285 : Simplifying Exponents

Example Question #286 : Simplifying Exponents

Example Question #282 : Simplifying Exponents

Example Question #287 : Simplifying Exponents

Example Question #288 : Simplifying Exponents

All Algebra II Resources

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