Exponents and Distributive Property Quiz

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Tags

CCSS.HSF-IF.C.8B

Answer explanation

The expression x^{-3} can be simplified using the property of exponents that states a^{-n} = \frac{1}{a^n}. Therefore, x^{-3} simplifies to \frac{1}{x^3}, which is the correct answer.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To multiply powers with the same base, add the exponents: \(2^3 \times 2^4 = 2^{3+4} = 2^7\). Thus, the correct answer is \(2^7\).

Answer explanation

To simplify 3(x^2 + 4), apply the distributive property: 3 * x^2 + 3 * 4 = 3x^2 + 12. Thus, the correct answer is 3x^2 + 12.

Tags

CCSS.6.EE.A.3

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Answer explanation

Any non-zero number raised to the power of 0 equals 1. Here, (x^2)^0 simplifies to 1, regardless of the value of x, as long as x is not zero.

Answer explanation

To simplify \(4^{-2}\), use the property \(a^{-n} = \frac{1}{a^n}\). Thus, \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\). The correct answer is \(\frac{1}{16}\).

Answer explanation

To simplify the expression a^3 × a^{-5}, use the property a^m × a^n = a^{m+n}. Here, 3 + (-5) = -2, so the result is a^{-2}, which matches the correct answer.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To find the value of (2)^3, we calculate 2 multiplied by itself three times: 2 x 2 x 2 = 8. Therefore, the correct answer is 8.

Answer explanation

To simplify, note that $5^0 = 1$ and $3^{-1} = \frac{1}{3}$. Thus, $5^0 \times 3^{-1} = 1 \times \frac{1}{3} = \frac{1}{3}$. The correct answer is $\frac{1}{3}$.

Answer explanation

To simplify (y^{-2})^3, use the power of a power rule: multiply the exponents. This gives y^{-2*3} = y^{-6}. Thus, the correct answer is y^{-6}.

Tags

CCSS.HSA.APR.A.1