Simplify the Expression: a^-3 × y^7 × a^-4 × y^-5 Using Exponent Rules

Question

Reduce the following equation:

$a^{-3}\times y^7\times a^{-4}\times y^{-5}=$

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of exponents with equal bases (A)

00:06 equals the same base raised to the sum of the exponents (N+M)

00:11 Let's identify the equal bases

00:15 Let's apply this formula to our exercise, one operation at a time

00:20 We'll maintain the base and add together the exponents

00:32 This is the solution

To simplify the given expression $a^{-3} \times y^7 \times a^{-4} \times y^{-5}$ , we will apply the exponent rules.

First, let's handle the terms involving the base $a$ :

$a^{-3} \times a^{-4}$

According to the rule $x^m \times x^n = x^{m+n}$ , we add the exponents:

$a^{-3} \times a^{-4} = a^{-3 + (-4)} = a^{-7}$

Next, consider the terms involving the base $y$ :

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

Using the same exponent rule:

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

The entire expression now becomes:

$a^{-7} \times y^2$

Thus, the simplified form of the given expression is $a^{-7} \times y^2$ .

$a^{-7}\times y^2$