Question

(7^3) *7^7 __________(7^5)^4​

Answer 1

$\frac{( {7}^{3}) \times {7}^{7} }{ {( {7}^{5} )}^{4} } = \frac{ {7}^{3 + 7} }{ {7}^{5 \times 4} } = \frac{ {7}^{10} }{ {7}^{20} } = \frac{ 1}{ {7}^{10} }$

Answer 2

$\frac{ {7}^{3} \times {7}^{7} }{ {( {7}^{5}) }^{4} } = \frac{ {7}^{10} }{ {7}^{20} } = \frac{1}{ {7}^{10} } = {7}^{ - 10}$

Answer 3

To simplify the expression, we can use the properties of exponents. Let's break down the expression step by step:

First, we have (7^3) * (7^7). Since the base (7) is the same in both terms, we can add the exponents:

7^3 * 7^7 = 7^(3 + 7) = 7^10.

Next, we have (7^5)^4. To simplify this, we multiply the exponent outside (4) by the exponent inside (5):

(7^5)^4 = 7^(5 * 4) = 7^20.

Now we can rewrite the entire expression:

(7^3) * (7^7) / (7^5)^4 = 7^10 / 7^20.

When dividing two numbers with the same base, we subtract the exponents:

7^10 / 7^20 = 7^(10 - 20) = 7^(-10).

Therefore, the simplified form of the expression (7^3) * (7^7) / (7^5)^4 is 7^(-10).