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High School Math : How to use the product rule for exponents in pre-algebra

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Example Questions

Example Question #1 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the following expression.

$2^{3}*2^{5}$

Possible Answers:

$4^{8}$

$2^{2}$

$2^{15}$

$4^{15}$

$2^{8}$

Correct answer:

$2^{8}$

Explanation:

$2^{3}*2^{5}$

This expression is a product of exponents with like bases. In these situations, we should use the product rule, which states that we should add the exponents.

$2^3*2^5=2^{3+5}=2^8$

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Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify $2^{4}2^{12}$ without evaluating.

Possible Answers:

Cannot be simplified

$2^{14}$

$2^{16}$

$2^{24}$

$2^{8}$

Correct answer:

$2^{16}$

Explanation:

When multilping 2 numbers with exponents, if the bases are the same, they can be combined and the exponents add together.

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Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Evaluate $\dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}$

Possible Answers:

$x^{2x^{2}-5x+13}$

$\dpi{100} x^{4x^{2}-10x+26}$

$\dpi{100} x^{x^{2}-2x+6}$

$\dpi{100} x^{x^{2}-x+7}$

$x^{4x-7}$

Correct answer:

$x^{2x^{2}-5x+13}$

Explanation:

The quotient rule for exponents states that when like numbers are raised to a certain power, then their exponents are subtracted from one another.

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{(4x^{2}-3x+7)-(2x^{2}+2x-6)}$

Solve for the exponent equation.

$(4x^{2}-3x+7)-(2x^{2}+2x-6)=4x^{2}-3x+7-2x^{2}-2x+6$

Combine like terms.

$\rightarrow (2x^{2}-5x+13)$

Therefore,

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{2x^{2}-5x+13}$

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Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the expression.

(2x^2)(5x^3)

Possible Answers:

7x^5

10x^6

10x

10x^5

7x^6

Correct answer:

10x^5

Explanation:

Since all terms are being multiplied, we can simplify by grouping like terms together.

(2x^2)(5x^3)

(2*5)(x^2*x^3)

To simplify the variable, we can add the exponents according to exponential identities.

$(2*5)(x^{2+3})$

10x^5

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Example Question #4 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the expression.

(3x^2y)(2xy^2)^2

Possible Answers:

36x^4y^5

12x^4y^5

36x^9y^9

12x^9y^9

Correct answer:

12x^4y^5

Explanation:

(3x^2y)(2xy^2)^2

Begin by distributing the exponent into the parentheses. Remember that each term in the parentheses must be squared.

(3x^2y)(4x^2y^4)

All terms are now being multiplied. To make it simpler, we can re-group by like terms.

(3*4)(x^2*x^2)(y*y^4)

Multiplying exponential terms with the same base allows us to add the exponents.

$12x^{2+2}y^{1+4}=12x^4y^5$

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Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is a simplified expression of X³X²?

Possible Answers:

$X^{1}$

$X^{5}$

$X^{6}$

$X\cdot 6$

$X\cdot X^{2}$

Correct answer:

$X^{5}$

Explanation:

When you multiply two exponential expressions with the same base, add the exponents to simplify the expression.

$X^{3}X^{2}=X^{5}$

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Example Question #4 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is an alternate expression of X³Y³?

Possible Answers:

$(X\cdot Y)^{3}$

$(X\cdot Y)^{9}$

$(XY)^{6}$

$X^{6}$

$(X+Y)^{3}$

Correct answer:

$(X\cdot Y)^{3}$

Explanation:

When you are required to multiply exponential expressions with different bases but the same exponent, you can simplify the expression by adding parentheses and only using the exponent one time.

$X^{3}Y^{3}=(X\cdot Y)^{3}$

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Example Question #5 : How To Use The Product Rule For Exponents In Pre Algebra

Which of the following is equivalent to the expression:

$3^{6}\cdot3^{-4}$ ?

Possible Answers:

$\frac{1}{9}$

$\frac{1}{27}$

Correct answer:

Explanation:

Recall that when we are multiplying exponential expressions with the same base, we add the exponents and keep the base the same. Additionally, remember that adding a negative number is equivalent to subtracting.

$3^{6} \cdot3^{-4} = 3^{6 + -4} = 3^{2} = 9$

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Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify (x^3)(x^8)

Possible Answers:

$x^{14}$

$x^{13}$

$x^{11}$

$x^{24}$

Correct answer:

$x^{11}$

Explanation:

When multiplying the same variable raised to different powers, add the powers of each term together. In this case, add and together to find the power of the answer, .

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Example Question #7 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the exponential expression.

$\small [(3x^2y^2)(4xy^3)]^0$

Possible Answers:

$\small 12x^3y^5$

undefined

Correct answer:

Explanation:

$\small [(3x^2y^2)(4xy^3)]^0$

Any number to the "zero" power is equal to .

(anything)^0=1

$\small [(3x^2y^2)(4xy^3)]^0=[12x^3y^5]^0=1$

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High School Math : How to use the product rule for exponents in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #4 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #3 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #4 : How To Use The Product Rule For Exponents In Pre Algebra

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