Multiplication of Powers: System of equations with no solution

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 powerInverse formulaVariable in the base of the powerNumber of termsCalculating powers with negative exponentsApplying the formulaUsing multiple rules
Question 1

Reduce the following equation:

\( 6^3\times6^{-4}\times6^7= \)

Question 2

\( \)

Simplify the following equation:

\( 5^8\times5^3= \)

Question 3

Simplify the following equation:

\( 3^4\times3^5= \)

Question 4

Simplify the following equation:

\( 2^2\times2^3= \)

Question 5

Simplify the following equation:

\( \)\( 9\times9^9= \)

Examples with solutions for Multiplication of Powers: System of equations with no solution

Exercise #1

Reduce the following equation:

63×6−4×67= 6^3\times6^{-4}\times6^7=

Step-by-Step Solution

To solve the expression 63×6−4×67 6^3 \times 6^{-4} \times 6^7 , we need to apply the rules of exponents, specifically the multiplication of powers. When we multiply powers with the same base, we add their exponents.

First, let's identify the base and the exponents in the expression:

  • The base is 6.

  • The exponents are 3, -4, and 7.

Using the exponent multiplication rule, we sum the exponents:

63×6−4×67=63+(−4)+7 6^3 \times 6^{-4} \times 6^7= 6^{3 + (-4) + 7}

So, the solution is:

63−4+7 6^{3-4+7}

Answer

63−4+7 6^{3-4+7}

Exercise #2

Simplify the following equation:

58×53= 5^8\times5^3=

Video Solution

Answer

58+3 5^{8+3}

Exercise #3

Simplify the following equation:

34×35= 3^4\times3^5=

Video Solution

Answer

34+5 3^{4+5}

Exercise #4

Simplify the following equation:

22×23= 2^2\times2^3=

Video Solution

Answer

22+3 2^{2+3}

Exercise #5

Simplify the following equation:

9×99= 9\times9^9=

Video Solution

Answer

91+9 9^{1+9}

Question 1

Simplify the following equation:

\( 8^3\times8= \)

Question 2

Simplify the following equation:

\( \)\( 6^2\times6^8= \)

Question 3

Simplify the following equation:

\( \)\( 12\times12^2= \)

Question 4

Simplify the following equation:

\( 7^6\times7^6= \)

Question 5

Simplify the following equation:

\( \)\( 4^5\times4\times4^2= \)

Exercise #6

Simplify the following equation:

83×8= 8^3\times8=

Video Solution

Answer

83+1 8^{3+1}

Exercise #7

Simplify the following equation:

62×68= 6^2\times6^8=

Video Solution

Answer

62+8 6^{2+8}

Exercise #8

Simplify the following equation:

12×122= 12\times12^2=

Video Solution

Answer

121+2 12^{1+2}

Exercise #9

Simplify the following equation:

76×76= 7^6\times7^6=

Video Solution

Answer

76+6 7^{6+6}

Exercise #10

Simplify the following equation:

45×4×42= 4^5\times4\times4^2=

Video Solution

Answer

45+1+2 4^{5+1+2}

Question 1

Simplify the following equation:

\( 5^3\times5^6\times5^2= \)

Question 2

Simplify the following equation:

\( 9^7\times9^3\times9^5= \)

Question 3

Simplify the following equation:

\( \)\( 11^2\times11^3\times11^4= \)

Question 4

Simplify the following equation:

\( \)\( 2^1\times2^2\times2^3= \)

Question 5

Reduce the following equation:

\( 2^4\times2^{-2}\times2^3= \)

Exercise #11

Simplify the following equation:

53×56×52= 5^3\times5^6\times5^2=

Video Solution

Answer

53+6+2 5^{3+6+2}

Exercise #12

Simplify the following equation:

97×93×95= 9^7\times9^3\times9^5=

Video Solution

Answer

97+3+5 9^{7+3+5}

Exercise #13

Simplify the following equation:

112×113×114= 11^2\times11^3\times11^4=

Video Solution

Answer

112+3+4 11^{2+3+4}

Exercise #14

Simplify the following equation:

21×22×23= 2^1\times2^2\times2^3=

Video Solution

Answer

21+2+3 2^{1+2+3}

Exercise #15

Reduce the following equation:

24×2−2×23= 2^4\times2^{-2}\times2^3=

Video Solution

Answer

24−2+3 2^{4-2+3}

Question 1

Simplify the following equation:

\( 4^{-2}\times4^{-4}= \)

Question 2

Simplify the following equation:

\( 3^{-4}\times3^{-2}= \)

Question 3

Simplify the following equation:

\( 2^6\times2^{-3}= \)

Question 4

Insert the corresponding expression:

\( 8^4\times8\times8^{-1}= \)

Question 5

Insert the corresponding expression:

\( 7^{-2}\times7^{-3}\times7^5= \)

Exercise #16

Simplify the following equation:

4−2×4−4= 4^{-2}\times4^{-4}=

Video Solution

Answer

4−2−4 4^{-2-4}

Exercise #17

Simplify the following equation:

3−4×3−2= 3^{-4}\times3^{-2}=

Video Solution

Answer

3−4−2 3^{-4-2}

Exercise #18

Simplify the following equation:

26×2−3= 2^6\times2^{-3}=

Video Solution

Answer

26−3 2^{6-3}

Exercise #19

Insert the corresponding expression:

84×8×8−1= 8^4\times8\times8^{-1}=

Video Solution

Answer

84+1−1 8^{4+1-1}

Exercise #20

Insert the corresponding expression:

7−2×7−3×75= 7^{-2}\times7^{-3}\times7^5=

Video Solution

Answer

7−2−3+5 7^{-2-3+5}

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