(3+4)^0 + 3-5^-3
(-4)^-3 * (-2)^3
(23^3)^15
(3+4)^0 + 3-5^-3
= 1 + 3 - 1/125
= 499/125
(-4)^-3 * (-2)^3
= 1/(-4)^3 * (-2)^3
= -1/64 * (-8)
= 1/8
(23^3)^15
= 23^45
= very big .......(appr 1.9 x 10^61)
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To simplify these expressions, we need to follow the rules of exponents.
1. (3+4)^0 + 3 - 5^-3:
Step 1: Simplify the base inside parentheses: 3 + 4 = 7.
Step 2: Any number raised to the power of 0 equals 1. So (3+4)^0 becomes 1.
Step 3: Simplify 5^-3. To simplify a negative exponent, you need to take the reciprocal of the base raised to the positive power: 5^-3 = 1/5^3.
Step 4: Calculate 5^3 = 125, and then take the reciprocal: 1/125.
Step 5: Now we have 1 + 3 - 1/125.
Step 6: We can combine the integers: 1+3=4.
Step 7: So the final answer is 4 - 1/125.
2. (-4)^-3 * (-2)^3:
Step 1: Calculate -4 to the power of -3: (-4)^-3 = -1/(4^3).
Step 2: Simplify 4^3: 4^3 = 64.
Step 3: Take the reciprocal: 1/64.
Step 4: Calculate (-2)^3: -2^3 = -8.
Step 5: Multiply the two results: (-1/64) * (-8).
Step 6: When multiplying two negative numbers, the result is positive, so the final answer is 1/64 * 8.
3. (23^3)^15:
Step 1: To raise a number to a power, we need to multiply the exponents. So (23^3)^15 becomes 23^(3*15).
Step 2: Multiply the two exponents: 3*15 = 45.
Step 3: Calculate 23^45 using a calculator or a mathematical software.
Step 4: The final answer is 23^45.