Multiply Powers: Simplifying t^6 × 4^6 Expression

Question

Insert the corresponding expression:

t6×46= t^6\times4^6=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 A product where each factor is raised to that factor's power (N)
00:07 Can be converted to parentheses of the entire product raised to the factor (N)
00:11 We will apply this formula to our exercise
00:16 This is the solution

Step-by-Step Solution

To solve this problem, we'll utilize the property of exponents that states:

  • (an×bn)=(a×b)n(a^n \times b^n) = (a \times b)^n

This property allows us to combine terms that are each raised to the same power. In this case, we have:

  • t6t^6 and 464^6 both raised to the power of 6.

By applying the property, we can rewrite the expression:

t6×46=(t×4)6t^6 \times 4^6 = (t \times 4)^6.

This simplifies the original expression by combining the bases under a single exponent.

Therefore, the expression equivalent to t6×46 t^6 \times 4^6 is (t×4)6\left(t \times 4\right)^6.

Answer

(t×4)6 \left(t\times4\right)^6