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Algebra II : Simplifying Exponents

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Example Questions

Example Question #251 : Simplifying Exponents

Expand and simplify: [1+(2^2)^3]^2

Possible Answers:

531441

1089

4225

4096

4097

Correct answer:

4225

Explanation:

Evaluate the exponential term inside the bracket first. Use the product rule for exponents to simplify.

$(2^2)^3 = (2^2)(2^2)(2^2) = 2^{2\cdot 3} = 2^6 = 64$

The term inside the bracket becomes:

[1+64]^2

Simplify the term inside.

65^2 = 4225

The answer is: 4225

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Example Question #252 : Simplifying Exponents

Solve: $(4^{150})^{5}$

Possible Answers:

$1024^{155}$

$4^{180}$

$4^{750}$

$4^{155}$

$1024^{30}$

Correct answer:

$4^{750}$

Explanation:

When the quantity of the terms of a base raised to a power is also raised to a power, we can use the product rule for exponents to expand this expression.

$(X^Y)^Z = X^{YZ}$

Multiply the powers together.

$(4^{150})^{5} = 4^{150\cdot 5} = 4^{750}$

The answer is: $4^{750}$

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Example Question #251 : Simplifying Exponents

Simplify: (8x^3)^2

Possible Answers:

64x^6

8x^6

16x^5

16x^6

Correct answer:

64x^6

Explanation:

$When\ raising\ a\ power\ to\ a\ power\ multiply\ the\ exponents.$

(8x^3)^2=8^2x^(^3^*^2^)=64x^6

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Example Question #254 : Simplifying Exponents

Simplify the exponents: $(2^3)^{-2}+(4^0)^3$

Possible Answers:

$\frac{1}{2}$

$\frac{65}{64}$

$\frac{13}{12}$

128

Correct answer:

$\frac{65}{64}$

Explanation:

To simplify this expression, since the powers are outside of a quantity of a power, we can multiply the powers together according to the power rule.

$(x^a)^b = x^{ab}$

Simplify the expression.

$(2^3)^{-2}+(4^0)^3 = 2^{-6}+4^0$

Change the negative exponent into a fraction and simplify.

$2^{-6}+4^0 = \frac{1}{2^6}+1 = \frac{1}{64}+\frac{64}{64}$

The answer is: $\frac{65}{64}$

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Example Question #255 : Simplifying Exponents

Simplify: $(\frac{1}{3^3})^{-2}$

Possible Answers:

243

$\frac{1}{243}$

$\frac{1}{3}$

$\frac{1}{729}$

729

Correct answer:

729

Explanation:

The fraction inside the parentheses can be rewritten as a negative exponent.

$(\frac{1}{3^3})^{-2}=(3^{-3})^{-2}$

Using the power property of exponents, multiply both exponents together.

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

Simplify this value.

$3^6 = 3\cdot3\cdot3\cdot3\cdot3\cdot3 = 729$

The answer is: 729

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Example Question #256 : Simplifying Exponents

Simplify: $(3^{11}\cdot 3^{10})^3$

Possible Answers:

$3^{24}$

$3^{330}$

$3^{63}$

$3^{113}$

$9^{330}$

Correct answer:

$3^{63}$

Explanation:

Determine the inner term by using the additive rule of exponents. When the bases of a certain power are similar, the powers can be added.

$(3^{11}\cdot 3^{10})^3 =(3^{11+10})^3 = (3^{21})^3$

Use the power rule to simplify this term.

$(3^{21})^3 = 3^{21\times 3} = 3^{63}$

The answer is: $3^{63}$

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Example Question #252 : Simplifying Exponents

Simplify: $(2x^{55})^{2}$

Possible Answers:

$2x^{110}$

$4x^{110}$

$2x^{107}$

$4x^{57}$

$2x^{57}$

Correct answer:

$4x^{110}$

Explanation:

According to the rule of exponents, we can distribute the power of two by multiplying the powers.

$(2x^{55})^{2} = (2x^{55})(2x^{55}) = (2^{1\times 2}x^{55 \times 2})$

Simplify the terms.

The answer is: $4x^{110}$

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Example Question #71 : Distributing Exponents (Power Rule)

Simplify the exponent: $(2a^{120})^{5}$

Possible Answers:

$2a^{125}$

$32a^{125}$

$2a^{600}$

$16a^{600}$

$32a^{600}$

Correct answer:

$32a^{600}$

Explanation:

According to the property of the power rule for exponents,

$(x^a)^b = x^{a\times b}$

The exponents may be multiplied if the exponent is outside of the parentheses.

$(2a^{120})^{5} = 2^5 \cdot a^{120\times 5}$

The answer is: $32a^{600}$

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Example Question #72 : Distributing Exponents (Power Rule)

Simplify: $(a^2b^{25})^{20}$

Possible Answers:

$a^{22}b^{45}$

$a^{40}b^{400}$

$a^{22}b^{500}$

$\frac{a^{10}b^{5}}{2}$

$a^{40}b^{500}$

Correct answer:

$a^{40}b^{500}$

Explanation:

In order to simplify this, we will need to distribute the power of 20 across both powers inside the inner quantity.

$(a^2b^{25})^{20} = (a^{2\cdot 20}b^{25\cdot 20})$

Multiply the powers.

The answer is: $a^{40}b^{500}$

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Example Question #73 : Distributing Exponents (Power Rule)

Simplify: $(x^{35}\cdot x^{20})^{15}$

Possible Answers:

$x^{10500}$

$x^{70}$

$x^{715}$

$x^{825}$

$x^{80}$

Correct answer:

$x^{825}$

Explanation:

Simplify the inner quantity first.

When powers of the same base are multiplied together, the powers may be added.

$x^{35}\cdot x^{20} = x^{55}$

The expression becomes: $(x^{55})^{15}$

When the quantity of a power is raised to a certain power, the powers will need to be multiplied.

$(x^{55})^{15} =x^{55\times 15} = x^{825}$

The answer is: $x^{825}$

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Algebra II : Simplifying Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #251 : Simplifying Exponents

Example Question #252 : Simplifying Exponents

Example Question #251 : Simplifying Exponents

Example Question #254 : Simplifying Exponents

Example Question #255 : Simplifying Exponents

Example Question #256 : Simplifying Exponents

Example Question #252 : Simplifying Exponents

Example Question #71 : Distributing Exponents (Power Rule)

Example Question #72 : Distributing Exponents (Power Rule)

Example Question #73 : Distributing Exponents (Power Rule)

All Algebra II Resources

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