Which two expressions are equivalent to $$ 4^{7} imes 4^{-5} $$ ? A $$ \frac{1}{4^{-2}} $$ B $$ \frac{1}{4^{2}} $$ C $$ 4^{-35} $$ D $$ 4^{-2} $$ E $$ 4^{2} $$ F $$ 4^{12} $$

Question

Which two expressions are equivalent to $$ 4^{7} 	imes 4^{-5} $$ ? A $$ \frac{1}{4^{-2}} $$ B $$ \frac{1}{4^{2}} $$ C $$ 4^{-35} $$ D $$ 4^{-2} $$ E $$ 4^{2} $$ F $$ 4^{12} $$

UpStudy AI · Accepted Answer

We start with the given expression:

$$
4^7 \times 4^{-5}
$$

Using the law of exponents, when multiplying with the same base we add the exponents:

$$
4^7 \times 4^{-5} = 4^{7 + (-5)} = 4^2
$$

Thus, any expression equivalent to $$4^2$$ is equivalent to the original expression.

Now, we check the options:

- **Option A:** $$\frac{1}{4^{-2}}$$  
  Rewrite by recalling that $$\frac{1}{4^{-2}} = 4^{2}$$.

- **Option B:** $$\frac{1}{4^{2}}$$  
  This expression is equivalent to $$4^{-2}$$, which is not equal to $$4^2$$.

- **Option C:** $$4^{-35}$$  
  This is not equivalent to $$4^2$$.

- **Option D:** $$4^{-2}$$  
  This is not equivalent to $$4^2$$.

- **Option E:** $$4^{2}$$  
  This is precisely the expression we obtained.

- **Option F:** $$4^{12}$$  
  This is not equivalent to $$4^2$$.

Thus, the equivalent expressions are in options A and E.
The equivalent expressions are $$ \frac{1}{4^{-2}} $$ and $$ 4^{2} $$.

Which two expressions are equivalent to \( 4^{7} \times 4^{-5} \) ? A \( \frac{1}{4^{-2}} \) B \( \frac{1}{4^{2}} \) C \( 4^{-35} \) D \( 4^{-2} \) E \( 4^{2} \) F \( 4^{12} \)

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