Question

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

Answer 1

The given expression is $4^{3} \times 4^{x}$

By using the law of exponent which states that $a^{m} \times a^{n} = a^{m+n}$

$4^{3} \times 4^{x} = 4^{3+x}$

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

1. $4^{3} \times 4^{x} = 4^{3+x}$

This expression is equivalent to the given expression.

2. $(4 \times x)^{3} = (4x)^{3} = 64x^{3}$

This expression is not equivalent to the given expression.

3. $4^{3-x}$

This expression is not equivalent to the given expression.

4. $64 \times 4^{x} = (4)^{3} \times 4^{x}=4^{3+x}$

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.