Solve: 3² × y² Expression (Multiplying Squared Terms)

Question

Insert the corresponding expression:

32×y2= 3^2\times y^2=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 A product where each factor is raised to the power of that factor (N)
00:07 Can be converted to parentheses of the entire product raised to the power of the factor (N)
00:12 We will apply this formula to our exercise
00:18 This is the solution

Step-by-Step Solution

To solve the problem 32×y2= 3^2 \times y^2 = , we will make use of the power of a product rule, which helps simplify products with the same exponents.

The rule states that for any numbers a a and b b and any exponent m m , (am×bm)=(a×b)m(a^m \times b^m) = (a \times b)^m.

Using this rule, we can combine 32 3^2 and y2 y^2 into a single expression:

  • Identify the bases: We have a base of 3 and a base of y y , both raised to the power of 2.

  • Apply the formula, combining the bases under a common exponent: (3×y)2(3 \times y)^2.

This shows that 32×y2=(3×y)2 3^2 \times y^2 = \left(3 \times y\right)^2 .

Answer

(3×y)2 \left(3\times y\right)^2