Expand t^9: Writing Out the Ninth Power Expression

Question

Expand the following expression:

t9= t^9=

Video Solution

Solution Steps

00:00 Identify which expressions are equal to the original expression
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 We'll apply this formula to our exercise
00:23 We can observe that in the second expression, the operation is addition and not multiplication
00:26 Therefore the formula is not relevant to the second expression
00:31 We'll maintain the base and add together the exponents
00:39 This is the solution

Step-by-Step Solution

To expand the expression t9 t^9 , we will express it as a product of powers. Using the exponent rule, which states that you can multiply powers with the same base by adding their exponents, we need to find powers such that the sum of the exponents equals 9.

Let's consider the expression t4×t2×t3 t^4 \times t^2 \times t^3 . When we apply the multiplication rule of exponents with the same base t t , we have:

  • t9=t4×t2×t3 t^9 = t^4 \times t^2 \times t^3
  • Here, 4+2+3=9 4 + 2 + 3 = 9 , confirming that the sum of the exponents equals the original exponent.

Thus, the expanded form of t9 t^9 is indeed t4×t2×t3 t^4 \times t^2 \times t^3 , which confirms that this is the correct expansion.

Therefore, the solution to the problem is t4×t2×t3\boldsymbol{t^4 \times t^2 \times t^3}.

Answer

t4×t2×t3 t^4\times t^2\times t^3