Question

Which expressions are equivalent to 81^x

Answer 1

Expressions equivalent to
`81^x` are (A)
`(9*9)^x` and (D)
`9^(2x)`, as they both correctly apply the rule of exponents, reflecting the multiplication of exponents when a power is raised to another power.

To determine which expressions are equivalent to 81x, recall that 81 is a power of 9, specifically 92.

Raising a power to a power means you multiply the exponents.

So, 81x is (92)x = 92x.

Let's evaluate the given options:

A. (9*9)x or 81x, which is equivalent to the original expression.

B. 9*9x or 91+x, which is not equivalent since the exponents do not match.

C. 92 or 81, which is the base without the exponent x, thus not equivalent.

D. 92x, which matches our transformed expression and is equivalent.

E. 9*.x or 9x, which is not equivalent due to a missing power of 2.

F. 92*9x or 92+x, which is not equivalent as the exponents are not correctly multiplied.

From the options, A and D are equivalent to 81x.

The probable question may be:

Which expressions are equivalent to 81^x

A. (9.9)*

B. 9.9x

C. 92x

D. 9.92x

E. 9*.9x

F. 92.9x