Complete the Expression: 8⁵ × b⁵ × z⁵ Product Problem

Question

Insert the corresponding expression:

85×b5×z5= 8^5\times b^5\times z^5=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 A multiplication where each factor is raised to the power of that factor (N)
00:07 Can be converted to parentheses of the entire multiplication raised to the power of the factor (N)
00:14 Apply this formula to our exercise
00:20 This is the solution

Step-by-Step Solution

To solve the problem, we need to condense the given expression using the rule for the power of a product.

Given is the expression: 85×b5×z5 8^5 \times b^5 \times z^5 .

We notice that all the bases 88, bb, and zz have an exponent of 5.

By the Power of a Product Rule, which states (a×b×c)n=an×bn×cn(a \times b \times c)^n = a^n \times b^n \times c^n, we can rewrite the product of these terms as a single product raised to the power of 5.

Therefore, the expression 85×b5×z58^5 \times b^5 \times z^5 can be rewritten in a single exponent form as:

(8×b×z)5 \left(8 \times b \times z\right)^5 .

The correct rewrite of the expression is (8×b×z)5\left(8 \times b \times z\right)^5.

Answer

(8×b×z)5 \left(8\times b\times z\right)^5