Question

Which expressions are equivalent to
5^2/5^8

Answer 1

Answer:

Explanation:

To find the equivalent expressions to 5²/5⁸, we can use the Laws of Exponents.

First, apply the quotient rule to the given exponential expression:

Now, apply the negative exponent rule:

Therefore, answer option A is an equivalent expression.

To find the other equivalent expression, rewrite the exponent of 5⁻⁶ as 2 · (-3):

Now, we can apply the power of a power rule:

Therefore, answer option D is also an equivalent expression.

Explanation:

Answer 2

`\textsf{A)} \quad (1)/(5^6)`

`\textsf{D)} \quad \left(5^2\right)^(-3)`

Explanation:

To find the equivalent expressions to 5²/5⁸, we can use the Laws of Exponents.

`\boxed{\begin{array}{rl}\underline{\sf Laws\;of\;Exponents}\\\\\sf Product:&a^m * a^n=a^(m+n)\\\\\sf Quotient:&a^m / a^n=a^(m-n)\\\\\sf Power\;of\;a\;Power:&(a^m)^n=a^(mn)\\\\\end{array}}`

First, apply the quotient rule to the given exponential expression:

`(5^2)/(5^8)=5^(2-8)=5^(-6)`

Now, apply the negative exponent rule:

`5^(-6)=(1)/(5^6)`

Therefore, answer option A is an equivalent expression.

To find the other equivalent expression, rewrite the exponent of 5⁻⁶ as 2 · (-3):

`5^(-6)=5^(2 \cdot(-3))`

Now, we can apply the power of a power rule:

`5^(-6)=5^(2 \cdot(-3))=\left(5^2\right)^(-3)`

Therefore, answer option D is also an equivalent expression.