Simplify 7^6 × 7^6: Exponent Multiplication Practice

Exponent Multiplication with Same Base

Simplify the following equation:

76×76= 7^6\times7^6=

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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, multiplying exponents with an equal base (A)
00:07 equals the same base raised to the sum of the exponents (N+M)
00:11 We will apply this formula to our exercise
00:14 We will add up the exponents and raise them to this power
00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Simplify the following equation:

76×76= 7^6\times7^6=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given expression.

  • Step 2: Recognize and apply the exponent multiplication rule.

  • Step 3: Simplify the expression by adding the exponents.

Now, let's work through each step:
Step 1: The expression given is 76×76 7^6 \times 7^6 .
Step 2: Since the bases are the same, apply the exponent rule: am×an=am+n a^m \times a^n = a^{m+n} .
Step 3: By adding the exponents, we have 6+6=12 6 + 6 = 12 .

Therefore, the simplified expression is 76+6 7^{6+6} or 712 7^{12} .

This corresponds to choice 2.

Thus, the solution to the problem is 76+6 7^{6+6} .

3

Final Answer

76+6 7^{6+6}

Key Points to Remember

Essential concepts to master this topic
  • Rule: When multiplying powers with same base, add the exponents
  • Technique: 76×76=76+6=712 7^6 \times 7^6 = 7^{6+6} = 7^{12}
  • Check: Count total factors: six 7s times six 7s equals twelve 7s ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying the exponents instead of adding them
    Don't calculate 76×76=76×6=736 7^6 \times 7^6 = 7^{6\times6} = 7^{36} ! This confuses multiplication of powers with raising a power to a power. Always add exponents when multiplying powers with the same base.

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

Why do I add the exponents instead of multiplying them?

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When you multiply 76×76 7^6 \times 7^6 , you're combining six 7s with six more 7s, giving you twelve 7s total. That's why it becomes 712 7^{12} !

What's the difference between 76+6 7^{6+6} and 712 7^{12} ?

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They're exactly the same! 76+6 7^{6+6} shows the work step, while 712 7^{12} is the simplified form. Both answers are correct.

When do I multiply exponents instead of adding them?

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You multiply exponents when you have a power raised to another power, like (76)6=76×6=736 (7^6)^6 = 7^{6\times6} = 7^{36} . Notice the parentheses make a big difference!

What if the bases were different, like 76×56 7^6 \times 5^6 ?

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When bases are different, you cannot combine the exponents. The expression 76×56 7^6 \times 5^6 stays as is, or you could write it as (7×5)6=356 (7 \times 5)^6 = 35^6 .

How can I remember this rule?

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Think of exponents as counting repeated multiplication. 76 7^6 means "multiply 7 six times," so 76×76 7^6 \times 7^6 means "multiply 7 a total of 6 + 6 = 12 times."

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