Solve the expression 15⋅8^0/5+4(7^0−6)
We'll follow the order of operations (also known as PEMDAS) to solve this expression:
First, we start by evaluating the exponent.
8^0 = 1 (Any number raised to the power of 0 is 1)
Now let's calculate the expression step by step:
15⋅1/5 + 4(1 − 6)
Next, let's simplify inside each parenthesis:
15⋅1/5 + 4(-5)
Now, let's multiply:
3 + (-20)
Finally, let's add:
3 - 20 = -17
Therefore, the solution to the expression 15⋅8^0/5+4(7^0−6) is -17.
Use the Power Rule of Exponents to simplify (10^3)^6 .
To simplify (10^3)^6 using the Power Rule of Exponents, we multiply the exponents.
The Power Rule of Exponents states that for any positive numbers a and b and any integers m and n, (a^m)^n = a^(m * n).
Applying this rule to our expression:
(10^3)^6 = 10^(3 * 6) = 10^18.
Therefore, the expression (10^3)^6 simplifies to 10^18.
Use the Power Rule of Exponents to create a simplified equivalent expression for (194)9 .
To create a simplified equivalent expression for (194)9 using the Power Rule of Exponents, we raise the base 194 to the power of 9.
According to the Power Rule of Exponents, for any positive number a and any integers m and n, (a^m)^n = a^(m * n).
Applying this rule to our expression:
(194)^9 = 194^(1 * 9) = 194^9.
Therefore, the simplified equivalent expression for (194)9 is 194^9.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .
To create a simplified equivalent expression for (19^4)^9 using the Power Rule of Exponents, we multiply the exponents.
According to the Power Rule of Exponents, for any positive number a and any integers m and n, (a^m)^n = a^(m * n).
In this case, we have (19^4)^9.
We multiply the exponents:
(19^4)^9 = 19^(4 * 9) = 19^36.
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
Apply the Property of Negative Integer Exponents to solve 7−3 . The answer should not contain any exponent expression or decimals.(1 point)
The Property of Negative Integer Exponents states that for any non-zero number a and any negative integer n, a^(-n) = 1 / a^n.
Applying this property to our expression:
7^(-3) = 1 / 7^3.
Now, let's simplify 7^3:
7^3 = 7 * 7 * 7 = 343.
Therefore, 7^(-3) = 1 / 343.
Hence, the solution to 7^(-3) in terms of fractions and without any exponent expression or decimals is 1/343.