Simplify the following:
50 × 4-1 + 8138^{\dfrac{1}{3}}831
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Given,
⇒50×4−1+813=1×4−1+(23)13=1×14+2=1+84=94=214.\Rightarrow 5^0 \times 4^{-1} + 8^{\dfrac{1}{3}} = 1 \times 4^{-1} + (2^3)^{\dfrac{1}{3}} \\[1em] = 1 \times \dfrac{1}{4} + 2 \\[1em] = \dfrac{1 + 8}{4} \\[1em] = \dfrac{9}{4} \\[1em] = 2\dfrac{1}{4}.⇒50×4−1+831=1×4−1+(23)31=1×41+2=41+8=49=241.
Hence, 50×4−1+813=2145^0 \times 4^{-1} + 8^{\dfrac{1}{3}} = 2\dfrac{1}{4}50×4−1+831=241.
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(4×107)(6×10−5)8×1010\dfrac{(4 \times 10^7)(6 \times 10^{-5})}{8 \times 10^{10}}8×1010(4×107)(6×10−5)
3ab−1+2ba−1\dfrac{3a}{b^{-1}} + \dfrac{2b}{a^{-1}}b−13a+a−12b
(8125)−13\Big(\dfrac{8}{125}\Big)^{-\dfrac{1}{3}}(1258)−31
(0.027)−13(0.027)^{-\dfrac{1}{3}}(0.027)−31
