Simplify t^7 × t^2: Exponent Multiplication Practice

Question

Reduce the following equation:

t7×t2= t^7\times t^2=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:06 equals the same base raised to the sum of the exponents (N+M)
00:09 We will apply this formula to our exercise
00:12 We'll maintain the base and add the exponents together
00:15 This is the solution

Step-by-Step Solution

To solve the problem of simplifying t7×t2 t^7 \times t^2 , we follow these steps:

  • Step 1: Identify the base and the exponents. Here, the base is t t , the first exponent is 7, and the second exponent is 2.
  • Step 2: Apply the exponent rule for multiplying powers with the same base, which states am×an=am+n a^m \times a^n = a^{m+n} .
  • Step 3: Add the exponents: 7+2=9 7 + 2 = 9 .
  • Step 4: Write the simplified expression: t9 t^9 .

Therefore, after applying the exponent rule, the simplified form of the expression is t9 t^9 .

The correct choice among the given options is not specifically listed, but the simplification corresponds to t7+2 t^{7+2} before explicitly adding to get t9 t^9 .

Answer

t7+2 t^{7+2}