Which expressions are equivalent to (5^(2))/(5^(8)) ? Choose 2 answers: (A) (1)/(5^(6)) B 1^(-6) c (5^(2))^(-3) D (5^(2))^(-8)

Simplify Expression: Simplify the expression (5^(2))/(5^(8)) using the laws of exponents. When dividing powers with the same base, subtract the exponents. (5^(2))/(5^(8)) = 5^(2-8) = 5^(-6)Compare with Options: Compare the simplified expression 5^(-6) with the given options. Option (A) is (1)/(5^(6)), which is equivalent to 5^(-6) because any positive number raised to a negative exponent is the reciprocal of that number raised to the positive exponent.Check Option (A): Check option (B) which is 1^(-6). 1 raised to any power is always 1, so 1^(-6) = 1, which is not equivalent to 5^(-6).Check Option (B): Check option (C) which is (5^(2))^(-3). Using the laws of exponents, when raising a power to a power, multiply the exponents. (5^(2))^(-3) = 5^(2*(-3)) = 5^(-6), which is equivalent to the original expression.Check Option (C): Check option (D) which is (5^(2))^(-8). Using the laws of exponents, when raising a power to a power, multiply the exponents. (5^(2))^(-8) = 5^(2*(-8)) = 5^(-16), which is not equivalent to the original expression.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expressions are equivalent to $\frac{5^{2}}{5^{8}}$ ? $\newline$ Choose $1$ answers: $\newline$ (A) $\frac{1}{5^{6}}$ $\newline$ (B) $1^{-6}$ $\newline$ (C) $5^{2}$ ^{ $-3$ } $\newline$ (D) $5^{2}$ ^{ $-8$ }

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

\frac{5^{2}}{5^{8}}

\newline

Choose

1

answers:

\newline

(A)

\frac{1}{5^{6}}

\newline

(B)

1^{-6}

\newline

(C)

5^{2}

-3

}

\newline

(D)

5^{2}

-8

}

Simplify Expression: Simplify the expression $(5^{2})/(5^{8})$ using the laws of exponents. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $(5^{2})/(5^{8}) = 5^{2-8} = 5^{-6}$
Compare with Options: Compare the simplified expression $5^{-6}$ with the given options. $\newline$ Option (A) is $(1)/(5^{6})$ , which is equivalent to $5^{-6}$ because any positive number raised to a negative exponent is the reciprocal of that number raised to the positive exponent.
Check Option (A): Check option (B) which is $1^{-6}$ . $1$ raised to any power is always $1$ , so $1^{-6} = 1$ , which is not equivalent to $5^{-6}$ .
Check Option (B): Check option (C) which is $(5^{2})^{(-3)}$ . $\newline$ Using the laws of exponents, when raising a power to a power, multiply the exponents. $\newline$ $(5^{2})^{(-3)} = 5^{2*(-3)} = 5^{-6}$ , which is equivalent to the original expression.
Check Option (C): Check option (D) which is $(5^{2})^{(-8)}$ . $\newline$ Using the laws of exponents, when raising a power to a power, multiply the exponents. $\newline$ $(5^{2})^{(-8)} = 5^{2*(-8)} = 5^{-16}$ , which is not equivalent to the original expression.