Use the Product Rule of Exponents to simplify
Use the Product Rule of Exponents to simplify 6^10 x 6^5 (put answer in exponent form)
Find the numerical equivalent of 8^9 x 8^-6
Find the value of x to make this exponential equation true…
5^x ÷ 5^5 = 5^12
Use the Power Rule of Exponents to simplify (9^3)^6 . Answer in exponent form.
Apply the Properties of Integer Exponents to generate equivalent expressions to
(6^-3)^7 x 6^20
━━━━━━━━ answer as improper fraction. (this is a fraction problem..numerator above the line and denominator below it)
6^-2
1. Using the Product Rule of Exponents, we can simplify 6^10 x 6^5 as 6^(10+5), which is equal to 6^15.
2. The numerical equivalent of 8^9 x 8^-6 can be found by applying the Quotient Rule of Exponents. We subtract the exponents to get 8^(9-6), which simplifies to 8^3. Therefore, the numerical equivalent is 512.
3. To find the value of x in the exponential equation 5^x ÷ 5^5 = 5^12, we can apply the Quotient Rule of Exponents. By subtracting the exponents, we have 5^(x-5) = 5^12. Since the bases are the same, x-5 must equal 12. Solving for x gives x = 17.
4. Using the Power Rule of Exponents, we can simplify (9^3)^6 as 9^(3*6), which simplifies to 9^18.
5. Applying the Properties of Integer Exponents, we can simplify (6^-3)^7 x 6^20 as 6^(-3*7) x 6^20. This simplifies to 6^(-21) x 6^20. Using the Product Rule of Exponents, we can add the exponents to get 6^(-21+20), which is equal to 6^(-1).
6. In improper fraction form, 6^-2 can be rewritten as 1/6^2 or 1/36.
1. To simplify 6^10 x 6^5 using the Product Rule of Exponents, you add the exponents together. Therefore, the simplified expression is 6^(10 + 5), which is equal to 6^15.
2. To find the numerical equivalent of 8^9 x 8^-6, you subtract the exponent of the second term from the exponent of the first term. Therefore, the expression simplifies to 8^(9 - 6) or 8^3.
3. To find the value of x in the equation 5^x ÷ 5^5 = 5^12, you subtract 5 from both sides of the equation to get 5^x = 5^(12 - 5), which simplifies to 5^x = 5^7. Since the base is the same, the exponents must be equal as well. Therefore, x = 7.
4. To simplify (9^3)^6 using the Power Rule of Exponents, you multiply the exponents together. Therefore, the simplified expression is 9^(3 * 6) or 9^18.
5. To simplify (6^-3)^7 x 6^20 using the Properties of Integer Exponents, you multiply the exponents together for both terms. Therefore, the expression becomes 6^(-3 * 7) x 6^20, which is 6^(-21) x 6^20. Applying the Property of Exponents that states a^(-n) = 1 / a^n, you can rewrite the expression as 1 / 6^(21 - 20) or 1 / 6^1, which simplifies to 1 / 6.
6. To simplify 6^-2 using the Properties of Integer Exponents, you apply the Property that states a^(-n) = 1 / a^n. Therefore, 6^-2 is equal to 1 / 6^2, which is equal to 1 / 36.
To simplify an expression using the Product Rule of Exponents, you add the exponents when multiplying two terms with the same base.
1) 6^10 x 6^5 = 6^(10+5) = 6^15
To find the numerical equivalent of an expression with exponents, you simply evaluate the base raised to the power.
2) 8^9 x 8^-6 = (8^9) / (8^6) = 8^(9-6) = 8^3 = 512
To solve an exponential equation, you can use the property that states if two powers with the same base are equal, then their exponents must be equal as well.
3) 5^x ÷ 5^5 = 5^(x-5) = 5^12
By setting the exponents equal, you have x - 5 = 12. Solving for x, you get x = 17.
To simplify an expression using the Power Rule of Exponents, you multiply the exponents when raising a power to another power.
4) (9^3)^6 = 9^(3*6) = 9^18
To simplify an expression with negative exponents, you can use the property that states a negative exponent can be converted to a positive exponent by taking its reciprocal.
5) (6^-3)^7 x 6^20 = (1/6^3)^7 x 6^20 = 1/(6^(3*7)) x 6^20 = 1/6^21
To express the answer as an improper fraction, you can write it as the numerator above the line and the denominator below it.
6) 6^-2 = 1/6^2 = 1/36