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

Q: Why do I add the exponents instead of multiplying them?

Think of exponents as counting repeated multiplication. $ t^7 $ means t multiplied 7 times, and $ t^2 $ means t multiplied 2 times. When you multiply them together, you get t multiplied 7 + 2 = 9 times total!

Q: What's the difference between this and raising a power to a power?

Great question! $ t^7 \times t^2 $ (multiplying) uses addition: add exponents. But $ (t^7)^2 $ (power to a power) uses multiplication: multiply exponents to get $ t^{14} $.

Q: What if the bases were different, like t⁷ × s²?

You cannot combine different bases! $ t^7 \times s^2 $ stays as $ t^7s^2 $. The exponent rules only work when the bases are exactly the same.

Q: Is t^(7+2) the same as t^9?

Yes! $ t^{7+2} $ is just the intermediate step showing the work. You should always simplify by calculating 7 + 2 = 9 to get the final answer $ t^9 $.

Q: How can I remember when to add vs multiply exponents?

Use this memory trick: Same base × same base = ADD exponents. Power to a power = MULTIPLY exponents. The operation you see (× or parentheses) tells you what to do!

Exponent Rules with Same Base Multiplication

Reduce the following equation:

$t^7\times t^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

Reduce the following equation:

$t^7\times t^2=$

Step-by-step solution

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

Step 1: Identify the base and the exponents. Here, the base is $t$ , 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 $a^m \times a^n = a^{m+n}$ .
Step 3: Add the exponents: $7 + 2 = 9$ .
Step 4: Write the simplified expression: $t^9$ .

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

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

Final Answer

$t^{7+2}$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying same bases, add the exponents together
Technique: $t^7 \times t^2 = t^{7+2} = t^9$
Check: Count total factors: t·t·t·t·t·t·t·t·t = 9 t's ✓

Common Mistakes

Avoid these frequent errors

Multiplying the exponents instead of adding them
Don't multiply 7 × 2 = 14 to get $t^{14}$ ! This confuses the power rule with the product rule and gives a completely wrong answer. Always add exponents when multiplying same bases: $t^7 \times t^2 = t^{7+2} = t^9$ .

Practice Quiz

Test your knowledge with interactive questions

$(3\times4\times5)^4=$

FAQ

Everything you need to know about this question

Why do I add the exponents instead of multiplying them?

Think of exponents as counting repeated multiplication. $t^7$ means t multiplied 7 times, and $t^2$ means t multiplied 2 times. When you multiply them together, you get t multiplied 7 + 2 = 9 times total!

What's the difference between this and raising a power to a power?

Great question! $t^7 \times t^2$ (multiplying) uses addition: add exponents. But $(t^7)^2$ (power to a power) uses multiplication: multiply exponents to get $t^{14}$ .

What if the bases were different, like t⁷ × s²?

You cannot combine different bases! $t^7 \times s^2$ stays as $t^7s^2$ . The exponent rules only work when the bases are exactly the same.

Is t^(7+2) the same as t^9?

Yes! $t^{7+2}$ is just the intermediate step showing the work. You should always simplify by calculating 7 + 2 = 9 to get the final answer $t^9$ .

How can I remember when to add vs multiply exponents?

Use this memory trick: Same base × same base = ADD exponents. Power to a power = MULTIPLY exponents. The operation you see (× or parentheses) tells you what to do!

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