Question

Which equations are equivalent to the expression below ? Check all that apply

4^3 * 4^x
A. 4^3 * 4^x
B. (4 * x )^3
C. 4^3-x
D.64 * 4^x
E. 4^3x
F.16^3x

Answer 1

The given expression is
`4^(3) * 4^(x)`

By using the law of exponent which states that
`a^(m) * a^(n) = a^(m+n)`

`4^(3) * 4^(x) = 4^(3+x)`

We need to find the equivalent expression for the given expression from the given expressions.

1.
`4^(3) * 4^(x) = 4^(3+x)`

This expression is equivalent to the given expression.

2.
`(4 * x)^(3) = (4x)^(3) = 64x^(3)`

This expression is not equivalent to the given expression.

3.
`4^(3-x)`

This expression is not equivalent to the given expression.

4.
`64 * 4^(x) = (4)^(3) * 4^(x)=4^(3+x)`

This expression is equivalent to the given expression.

5.
`4^(3x)`

This expression is not equivalent to the given expression.

6.
`16^(3x)=(4^(2))^(3x)=4^(6x)`

This expression is not equivalent to the given expression.