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
To simplify 6^10 x 6^5, we can use the Product Rule of Exponents, which states that when multiplying two exponential expressions with the same base, you keep the base and add the exponents.
Therefore, 6^10 x 6^5 can be simplified to 6^(10+5) = 6^15.
To find the numerical equivalent of 8^9 x 8^-6, we can again apply the Product Rule of Exponents. Since 8^-6 can be written as 1/8^6, we have:
8^9 x 8^-6 = 8^9 x (1/8^6) = 8^(9-6) = 8^3.
Therefore, the numerical equivalent of 8^9 x 8^-6 is 8^3.
To find the value of x in the exponential equation 5^x ÷ 5^5 = 5^12, we can use the Quotient Rule of Exponents, which states that when dividing exponential expressions with the same base, you keep the base and subtract the exponents.
Therefore, 5^x ÷ 5^5 can be simplified to 5^(x-5) = 5^12.
To solve for x, we can equate the exponents:
x - 5 = 12.
Adding 5 to both sides, we get:
x = 17.
Therefore, the value of x that makes the equation true is x = 17.
To simplify 6^10 x 6^5 using the product rule of exponents, we add the exponents:
6^10 x 6^5 = 6^(10+5)
Therefore, the simplified expression is 6^15.
To find the numerical equivalent of 8^9 x 8^-6, we subtract the exponents:
8^9 x 8^-6 = 8^(9-6)
Simplifying further:
8^9 x 8^-6 = 8^3
Therefore, the numerical equivalent is 512 (since 8^3 = 8 x 8 x 8 = 512).
To find the value of x in the equation 5^x ÷ 5^5 = 5^12, we use the quotient rule of exponents:
5^x ÷ 5^5 = 5^(x-5)
Since this is equal to 5^12, we can set the exponents equal to each other:
x - 5 = 12
Solving for x, we add 5 to both sides:
x = 12 + 5
Therefore, the value of x that makes the exponential equation true is x = 17.
To simplify the expression 6^10 x 6^5 using the Product Rule of Exponents, we add the exponents together because we are multiplying the same base, which is 6 in this case. So, we can simplify it as follows:
6^10 x 6^5 = 6^(10+5) = 6^15
Therefore, the simplified expression in exponential form is 6^15.
To find the numerical equivalent of 8^9 x 8^-6, we again use the Product Rule of Exponents. When multiplying the same base and using the Product Rule, we add the exponents. Thus, we have:
8^9 x 8^-6 = 8^(9 + (-6)) = 8^3
Therefore, the numerical equivalent is 8^3, which is equal to 512.
To find the value of x to make the exponential equation 5^x ÷ 5^5 = 5^12 true, we use the Quotient Rule of Exponents. According to the Quotient Rule, when dividing the same base, we subtract the exponents. So, we have:
5^x ÷ 5^5 = 5^12
Using the Quotient Rule, we can rewrite the equation as:
5^(x-5) = 5^12
Since the bases are the same, for the equations to be true, the exponents must be equal. Therefore, we have:
x - 5 = 12
Solving for x, we add 5 to both sides of the equation:
x = 12 + 5 = 17
Therefore, the value of x that makes the equation true is 17.