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Use the Product Rule of Exponents to simplify 5^10 ⋅ 5^5 (1 point)
Find the numerical equivalent of 9^9 ⋅ 9^−6 .(1 point)
What is the missing exponent in the following equation? h450/h? = h215 (1 point)
Simplify 12^87÷12^25 .(1 point)
What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12 ?(1 point)
What is the value of 6.9−2^0 ?(1 point)
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0) .(2 points)
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I apologize for any confusion. Here are the step-by-step answers to your questions:
1. To simplify 5^10 ⋅ 5^5 using the Product Rule of Exponents, add the exponents since the base is the same: 5^(10+5) = 5^15.
2. To find the numerical equivalent of 9^9 ⋅ 9^(-6), use the Quotient Rule of Exponents which states that a^m / a^n = a^(m-n). Therefore, 9^9 ⋅ 9^(-6) = 9^(9-6) = 9^3 which is equal to 729.
3. To find the missing exponent in the equation h450/h? = h215, we can compare the bases of h. Since h is the same, we can equate the exponents. Therefore, ? = 450 - 215 = 235.
4. To simplify 12^87 ÷ 12^25, apply the Quotient Rule of Exponents which states that a^m / a^n = a^(m-n). In this case, 12^(87-25) = 12^62.
5. To find the missing number in the simplified exponential expression 7^? ÷ 7^5 = 7^12, we can apply the Quotient Rule of Exponents. Subtract the exponents and set it equal to the exponent on the right-hand side: ? - 5 = 12. Adding 5 to both sides gives us ? = 17.
6. The value of 6.9 - 2^0 can be simplified by evaluating 2^0, which is equal to 1. Therefore, 6.9 - 1 = 5.9.
7. Applying the Zero Power Rule to the expression 9⋅(−33)^0 + 3/2(8 − 27^0), any base (except 0) raised to the power of 0 is equal to 1. So, (-33)^0 becomes 1, and 27^0 also becomes 1. The expression simplifies to 9⋅1 + 3/2(8-1) = 9 + 3/2(7) = 9 + (3/2)(7) = 9 + 10.5 = 19.5.
Please let me know if you would like the step-by-step answers to the rest of the questions.
To solve these exponent problems, let's go step by step:
1. To simplify 5^10 ⋅ 5^5 using the Product Rule of Exponents, we add the exponents when multiplying powers with the same base. Therefore,
5^10 ⋅ 5^5 = 5^(10+5) = 5^15.
2. To find the numerical equivalent of 9^9 ⋅ 9^−6, we use the property that when multiplying powers with the same base, we add their exponents. So,
9^9 ⋅ 9^−6 = 9^(9+(-6)) = 9^3 = 729.
3. To find the missing exponent in the equation h450/h? = h215, we can rewrite it as an exponential equation using the property that a/b is the same as a * b^(-1). Therefore,
h450/h? = h215 can be written as h450 * h?^(-1) = h215.
From this, we know that h450 divided by h? is equal to h215. We can now use the division property of exponents, where a/b is the same as a * b^(-1). Therefore, the missing exponent is (-1).
4. To simplify 12^87 ÷ 12^25, we use the quotient rule of exponents. We subtract the exponents when dividing powers with the same base. Hence,
12^87 ÷ 12^25 = 12^(87-25) = 12^62.
5. To find the missing number in the simplified exponential expression 7^? ÷ 7^5 = 7^12, we use the quotient rule of exponents. Subtracting exponents gives
7^(?-5) = 7^12.
From this, we know that the missing number ? minus 5 must equal 12. So, ? = 17.
6. To find the value of 6.9−2^0, we simplify the expression according to the order of operations, which means we evaluate the exponent first. In this case, any number raised to the power of 0 is equal to 1. Hence,
6.9−2^0 = 6.9 - 1 = 5.9.
7. To apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0), we simplify the parts of the expression involving zero exponents. Any number (except 0) raised to the power of 0 is equal to 1. Hence,
9⋅(−33)^0+3/2(8−27^0) = 9⋅1 + 3/2(8-1) = 9 + 3/2(7) = 9 + 21/2 = 27/2.
I hope this helps! Let me know if you have more questions.