Multiplication of Powers: Inverse formula

Using the commutative lawCombination of different basesFactoring Out the Greatest Common Factor (GCF)Numbers as coefficientsPresenting powers with negative exponents as fractionsSolving the problemVariable in the exponent of the powerIdentify the greater valueVariables in the exponent of the powerVariable in the base of the powerNumber of termsCalculating powers with negative exponentsSystem of equations with no solutionApplying the formulaUsing multiple rules
Question 1

Expand the following equation:

\( 3^{12+10+5}= \)

Question 2

Expand the following equation:

\( 6^{3+2}= \)

Question 3

Expand the following equation:

\( 4^{4+6}= \)

Question 4

Expand the following equation:

\( 2^{2+5}= \)

Question 5

Expand the following equation:

\( 7^8= \)

Examples with solutions for Multiplication of Powers: Inverse formula

Exercise #1

Expand the following equation:

312+10+5= 3^{12+10+5}=

Step-by-Step Solution

To expand the equation 312+10+5 3^{12+10+5} , we will apply the rule of exponents that states: when you multiply powers with the same base, you can add the exponents. However, in this case, we are starting with a single term and want to represent it as a product of terms with the base being raised to each of the individual exponents given in the sum. Here’s a step-by-step explanation:

1. Start with the expression: 312+10+5 3^{12+10+5} .

2. Recognize that the exponents are added together. According to the property of exponents (Multiplication of Powers), we can express a single power with summed exponents as a product of powers:

3. Break down the exponents: 312+10+5=312×310×35 3^{12+10+5} = 3^{12} \times 3^{10} \times 3^5 .

4. As seen from the explanation: 312+10+5 3^{12+10+5} is expanded to the product 312×310×35 3^{12} \times 3^{10} \times 3^5 by expressing each part of the sum as an exponent with the base 3.

The final expanded form is therefore: 312×310×35 3^{12} \times 3^{10} \times 3^5 .

Answer

312×310×35 3^{12}\times3^{10}\times3^5

Exercise #2

Expand the following equation:

63+2= 6^{3+2}=

Video Solution

Answer

63×62 6^3\times6^2

Exercise #3

Expand the following equation:

44+6= 4^{4+6}=

Video Solution

Answer

44×46 4^4\times4^6

Exercise #4

Expand the following equation:

22+5= 2^{2+5}=

Video Solution

Answer

22×25 2^2\times2^5

Exercise #5

Expand the following equation:

78= 7^8=

Video Solution

Answer

None of the answers are correct

Question 1

Expand the following equation:

\( 9^{12}= \)

Question 2

Expand the following equation:

\( 8^4= \)

Question 3

Expand the following expression:

\( 7^6= \)

Question 4

Expand the following equation:

\( 8^{10}= \)

Question 5

Expand the following equation:

\( 6^{12}= \)

Exercise #6

Expand the following equation:

912= 9^{12}=

Video Solution

Answer

98×94 9^8\times9^4

Exercise #7

Expand the following equation:

84= 8^4=

Video Solution

Answer

All answers are correct

Exercise #8

Expand the following expression:

76= 7^6=

Video Solution

Answer

71×7×74 7^1\times7\times7^4

Exercise #9

Expand the following equation:

810= 8^{10}=

Video Solution

Answer

83×83×84 8^3\times8^3\times8^4

Exercise #10

Expand the following equation:

612= 6^{12}=

Video Solution

Answer

62×63×67 6^2\times6^3\times6^7

Question 1

Expand the following equation:

\( 5^4= \)

Question 2

Expand the following expression:

\( 6^{-8}= \)

Question 3

Expand the following expression:

\( 10^{-1}= \)

Question 4

Expand the following expression:

\( 5^{-3}= \)

Question 5

Expand the following expression:

\( 4^{-6}= \)

Exercise #11

Expand the following equation:

54= 5^4=

Video Solution

Answer

5×5×52 5\times5\times5^2

Exercise #12

Expand the following expression:

6−8= 6^{-8}=

Video Solution

Answer

A+B are correct

Exercise #13

Expand the following expression:

10−1= 10^{-1}=

Video Solution

Answer

10−11×1010 10^{-11}\times10^{10}

Exercise #14

Expand the following expression:

5−3= 5^{-3}=

Video Solution

Answer

A+B are correct

Exercise #15

Expand the following expression:

4−6= 4^{-6}=

Video Solution

Answer

Question 1

Insert the corresponding expression:

\( 9^{-7}= \)

Question 2

Expand the following expression:

\( b^7= \)

Question 3

Expand the following expression:

\( z^3= \)

Question 4

Expand the following equation:

\( x^{2+4}= \)

Question 5

Expand the following equation:

\( a^{3+5}= \)

Exercise #16

Insert the corresponding expression:

9−7= 9^{-7}=

Video Solution

Answer

9−4×9−2×9−1 9^{-4}\times9^{-2}\times9^{-1}

Exercise #17

Expand the following expression:

b7= b^7=

Video Solution

Answer

b1×b2×b4 b^1\times b^2\times b^4

Exercise #18

Expand the following expression:

z3= z^3=

Video Solution

Answer

A'+C' are correct

Exercise #19

Expand the following equation:

x2+4= x^{2+4}=

Video Solution

Answer

A+B are correct

Exercise #20

Expand the following equation:

a3+5= a^{3+5}=

Video Solution

Answer

a3×a5 a^3\times a^5