Multiplication of Powers: System of equations with no solution

Applying the formulaCalculating powers with negative exponentsCombination of different basesFactoring Out the Greatest Common Factor (GCF)Identify the greater valueInverse formulaNumber of termsNumbers as coefficientsPresenting powers with negative exponents as fractionsSolving the problemUsing multiple rulesUsing the commutative lawVariable in the base of the powerVariable in the exponent of the powerVariables in the exponent of the power
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:

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

Question 4

Simplify the following equation:

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

Question 5

Simplify the following equation:

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

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:

76×76= 7^6\times7^6=

Video Solution

Answer

76+6 7^{6+6}

Exercise #4

Simplify the following equation:

34×35= 3^4\times3^5=

Video Solution

Answer

34+5 3^{4+5}

Exercise #5

Simplify the following equation:

22×23= 2^2\times2^3=

Video Solution

Answer

22+3 2^{2+3}

Question 1

Simplify the following equation:

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

Question 2

Simplify the following equation:

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

Question 3

Simplify the following equation:

\( 8^3\times8= \)

Question 4

Simplify the following equation:

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

Question 5

Simplify the following equation:

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

Exercise #6

Simplify the following equation:

62×68= 6^2\times6^8=

Video Solution

Answer

62+8 6^{2+8}

Exercise #7

Simplify the following equation:

9×99= 9\times9^9=

Video Solution

Answer

91+9 9^{1+9}

Exercise #8

Simplify the following equation:

83×8= 8^3\times8=

Video Solution

Answer

83+1 8^{3+1}

Exercise #9

Simplify the following equation:

12×122= 12\times12^2=

Video Solution

Answer

121+2 12^{1+2}

Exercise #10

Simplify the following equation:

53×56×52= 5^3\times5^6\times5^2=

Video Solution

Answer

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

Question 1

Simplify the following equation:

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

Question 2

Simplify the following equation:

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

Question 3

Simplify the following equation:

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

Question 4

Simplify the following equation:

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

Question 5

Insert the corresponding expression:

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

Exercise #11

Simplify the following equation:

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

Video Solution

Answer

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

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:

21×22×23= 2^1\times2^2\times2^3=

Video Solution

Answer

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

Exercise #14

Simplify the following equation:

45×4×42= 4^5\times4\times4^2=

Video Solution

Answer

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

Exercise #15

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}

Question 1

Reduce the following equation:

\( y^9\times y^2\times y^3= \)

Question 2

Reduce the following equation:

\( a^2\times a^3= \)

Question 3

Reduce the following equation:

\( x^3\times x^4\times x^8= \)

Question 4

Reduce the following equation:

\( \)\( 8^a\times8^2\times8^x= \)

Question 5

Reduce the following equation:

\( \)\( 5^a\times5^{2a}\times5^{3a}= \)

Exercise #16

Reduce the following equation:

y9×y2×y3= y^9\times y^2\times y^3=

Video Solution

Answer

All answers are correct

Exercise #17

Reduce the following equation:

a2×a3= a^2\times a^3=

Video Solution

Answer

a2+3 a^{2+3}

Exercise #18

Reduce the following equation:

x3×x4×x8= x^3\times x^4\times x^8=

Video Solution

Answer

A'+C' are correct

Exercise #19

Reduce the following equation:

8a×82×8x= 8^a\times8^2\times8^x=

Video Solution

Answer

8a+2+x 8^{a+2+x}

Exercise #20

Reduce the following equation:

5a×52a×53a= 5^a\times5^{2a}\times5^{3a}=

Video Solution

Answer

5a+2a+3a 5^{a+2a+3a}

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